Amir D. Aczel has been closely associated with CERN and particle physics for a number of years and often consults on statistical issues relating to physics. He is also the author of 18 popular books on mathematics and science.

By now you’ve heard the news-non-news about the Higgs: there are hints of a Higgs—even “strong hints”—but no cigar (and no Nobel Prizes) yet. So what is the story about the missing particle that everyone is so anxiously waiting for?

Back in the summer, there was a particle physics conference in Mumbai, India, in which results of the search for the Higgs in the high-energy part of the spectrum, from 145 GeV (giga electron volts) to 466 GeV, were reported and nothing was found. At the low end of the energy spectrum, at around 120 GeV (a region of energy that attracted less attention because it had been well within the reach of Fermilab’s now-defunct Tevatron accelerator) there was a slight “bump” in the data, barely breaching the two-sigma (two standard deviations) bounds—which is something that happens by chance alone about once in twenty times (two-sigma bounds go with 95% probability, hence a one-in-twenty event is allowable as a fluke in the data). But since the summer, data has doubled: twice as many collision events had been recorded as had been by the time the Mumbai conference had taken place. And, lo and behold: the bump still remained!

This gave the CERN physicists the idea that perhaps that original bump was not a one-in-twenty fluke that happens by chance after all, but perhaps something far more significant. Two additional factors came into play as well: the new anomaly in the data at roughly 120 GeV was found by both competing groups at CERN: the CMS detector, and the ATLAS detector; and—equally important—when the range of energy is pre-specified, the statistical significance of the finding suddenly jumps from two-sigma to three-and-a-half-sigma!

This means that if you pre-specify that the Higgs must be “light” (in the low end of the energy spectrum, as, in fact, the Standard Model indicates), the chance that the data bump is a fluke quickly goes down to 1 in 5,000, and the probability that the Higgs boson actually exists jumps from a little over 95% to more than 99.98%–an excellent probability. By convention, however, physicists demand a five-sigma level of proof for all particle discoveries, which means a probability of 99.99997%. Such strict standards of proof would require a lot more data. So, at present, we have only “hints of a Higgs” and we are still waiting for the final, five-sigma word on the Higgs’ existence. But as Rolf Heuer, CERN’s director general, put: “We’ll be open all next year…” So stay tuned.

There’s a 99.99998% chance that the accelerator is making the same mistake over and over…

Jim Johnson

I thought the bump was supposed to be at 123-126 GeV.

Rich F

Oh, please, people! Read ‘em and weep: The odds the Higgs is there when they crack open up that data from next year, weighing in at around 123 Gev, are now set at 4999 chances in 5000. The house in Vegas thrives year after year on odds that are far worse than that. If only Wall Street were so reliable for payout on supposedly AAA investments, reeling in private funding for physics would be child’s play. Get a life!

chris y

a region of energy that attracted less attention because it had been well within the reach of Fermilab’s now-defunct Tevatron accelerator

So what were they doing wrong at Fermilab that they didn’t find it (if it’s there)?

Victor Grauer

Seems to me you’d need a lot more than a “bump” to determine that this is actually the Higgs. Especially since they seem to have no idea what mass to look for. Is there any reason this bump couldn’t represent some other particle? Why do they feel so confident it’s the Higgs?

http://amirdaczel.com Amir D. Aczel

Thanks for the great questions! So here are some attempts at answers: What CERN needs is luminosity (the term they use for how many protons collide per second). That lowers the standard errors and hence makes statistically significant what is true and (hopefully) washes out what is not true. The bump was indeed at the region specified: I used “around 120 GeV” as not to be too specific on something that is still not yet confirmed. Also: the two teams, ATLAS and CMS, found “bumps” not at exactly the same spot. Tevatron had an energy of 1.98 TeV (LHC now is at 7 TeV and going up to 14 in a couple of years from now). Since a TeV is 1,000 times more than a GeV, at roughly 120 GeV, Tevatron could conceivably have found a similar bump (and did). But because of luminosity issues, it was a tenuous bump. With increasing data from CERN and more scrutiny on the Fermilab data collected before closure of the Tevatron, hopefully the statistics will “converge” on the Higgs with very high probability (5-sigma) or the signal will shrink. About the Collider itself: It has repeatedly passed every test of quality and physicists have immense confidence in its performance (because it replicates with high accuracy everything that has been learned before through other accelerators). About Vegas: Oh well…what can I say? Physicists are just so much more exacting with data and probabilities and want to be far surer than odds at any game of chance.

scribbler

What effect, if any, does the discovery of the new chi b(3P) particle have on these findings? Do the Higgs results have to be adjusted for this new particle or are they separate/independent of each other?

Thanks in advance!

http://amirdaczel.com Amir D. Aczel

Good question, Scribbler! So, the new particle is a meson. A meson is an intermediate-sized particle made of two quarks (so it is not an elementary particle, like a quark, an electron, or a muon, for example). Pions, for example, are mesons made of the lightest quarks, and then mesons go up in mass from there (remember, there are three generations of quarks and leptons, in increasing mass). The new meson is of very high mass because it is made of very heavy quarks (thus requiring the energy of the LHC to create it). But you can “create” mesons simply by combinatorics: combine a quark with a given mass with an antiquark of a higher mass (higher generation quark) and you’ve got yourself a new meson. This new meson was, therefore, predictable by straightforward combinatorics. If you like abstract math, group theory has been especially useful in predicting new mesons, for example, the famous “Eightfold Way” of Murray Gell-Mann (which won him a Nobel when he predicted the Omega-minus meson) and Y. Ne’eman. Having said all this (as you can see), the Higgs mechanism and the Higgs boson are completely unaffected by this discovery. The chance that the Higgs exists is simply whatever it was before this new discovery. Happy New Year! Amir

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About Amir Aczel

Amir D. Aczel studied mathematics and physics at the University of California at Berkeley, where he was fortunate to meet quantum pioneer Werner Heisenberg. He also holds a Ph.D. in mathematical statistics. Aczel is a Guggenheim Fellow, a Sloan Foundation Fellow, and was a visiting scholar at Harvard in 2005-2007. He is the author of 18 critically acclaimed books on mathematics and science, several of which have been international bestsellers, including Fermat's Last Theorem, which was nominated for a Los Angeles Times Book Award in 1996 and translated into 31 languages. In his latest book, "Why Science Does Not Disprove God," Aczel takes issue with cosmologist Lawrence M. Krauss's theory that the universe emerged out of sheer "nothingness," countering the arguments using results from physics, cosmology, and the abstract mathematics of set theory.